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55 lines
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55 lines
2.5 KiB
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<p>Given an <code>m x n</code> <code>matrix</code>, return <em>a new matrix </em><code>answer</code><em> where </em><code>answer[row][col]</code><em> is the </em><em><strong>rank</strong> of </em><code>matrix[row][col]</code>.</p>
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<p>The <strong>rank</strong> is an <strong>integer</strong> that represents how large an element is compared to other elements. It is calculated using the following rules:</p>
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<ul>
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<li>The rank is an integer starting from <code>1</code>.</li>
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<li>If two elements <code>p</code> and <code>q</code> are in the <strong>same row or column</strong>, then:
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<ul>
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<li>If <code>p < q</code> then <code>rank(p) < rank(q)</code></li>
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<li>If <code>p == q</code> then <code>rank(p) == rank(q)</code></li>
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<li>If <code>p > q</code> then <code>rank(p) > rank(q)</code></li>
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</ul>
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</li>
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<li>The <strong>rank</strong> should be as <strong>small</strong> as possible.</li>
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</ul>
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<p>The test cases are generated so that <code>answer</code> is unique under the given rules.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank1.jpg" style="width: 442px; height: 162px;" />
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<pre>
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<strong>Input:</strong> matrix = [[1,2],[3,4]]
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<strong>Output:</strong> [[1,2],[2,3]]
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<strong>Explanation:</strong>
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The rank of matrix[0][0] is 1 because it is the smallest integer in its row and column.
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The rank of matrix[0][1] is 2 because matrix[0][1] > matrix[0][0] and matrix[0][0] is rank 1.
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The rank of matrix[1][0] is 2 because matrix[1][0] > matrix[0][0] and matrix[0][0] is rank 1.
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The rank of matrix[1][1] is 3 because matrix[1][1] > matrix[0][1], matrix[1][1] > matrix[1][0], and both matrix[0][1] and matrix[1][0] are rank 2.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank2.jpg" style="width: 442px; height: 162px;" />
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<pre>
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<strong>Input:</strong> matrix = [[7,7],[7,7]]
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<strong>Output:</strong> [[1,1],[1,1]]
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</pre>
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<p><strong>Example 3:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/10/18/rank3.jpg" style="width: 601px; height: 322px;" />
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<pre>
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<strong>Input:</strong> matrix = [[20,-21,14],[-19,4,19],[22,-47,24],[-19,4,19]]
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<strong>Output:</strong> [[4,2,3],[1,3,4],[5,1,6],[1,3,4]]
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>m == matrix.length</code></li>
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<li><code>n == matrix[i].length</code></li>
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<li><code>1 <= m, n <= 500</code></li>
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<li><code>-10<sup>9</sup> <= matrix[row][col] <= 10<sup>9</sup></code></li>
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</ul>
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